1. Start with the given set of FDs.

2. Add all the given FDs to the closure set.

3. Repeat the following steps until no new FDs can be derived:
a. For each FD in the closure set, apply the reflexivity axiom to add any trivial FDs.
b. For each pair of FDs in the closure set, apply the augmentation axiom to derive new FDs.
c. For each set of three FDs in the closure set that satisfy the transitivity condition, apply the transitivity axiom to derive new FDs.

4. Once no new FDs can be derived, the closure set represents the complete set of FDs that can be logically inferred from the given set.

For example, let's say we have the following set of FDs:

- A → B
- B → C

To find the closure, we start with the given set:

Closure = {A → B, B → C}

Applying the reflexivity axiom, we add any trivial FDs:

Closure = {A → B, B → C, A → A, B → B, C → C}

Next, we apply the augmentation axiom to derive new FDs:

Closure = {A → B, B → C, A → C, B → A}

Lastly, we check the transitivity condition and apply the transitivity axiom:

Closure = {A → B, B → C, A → C, B → A, A → A, B → B, C → C}

Now, the closure set contains all the FDs that can be logically derived from the given set.

The closure of a set of FDs is important in database design, normalization, and ensuring data integrity. It helps identify the complete set of relationships and dependencies among attributes in a relational database.

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